Two-settlement Systems for Electricity Markets under Network Uncertainty and Market Power

Transcription

1 Two-settlement Systems for Electrcty Markets under Network Uncertanty and Market Power Ransh Kamat Fnancal Engneerng Assocates, Inc Dwght Way Berkeley, CA USA Shmuel S. Oren Department of Industral Engneerng and Operatons Research 4135 Etcheverry Hall Unversty of Calforna at Berkeley Berkeley, CA USA ABSTRACT We analyze welfare and dstrbutonal propertes of a two-settlement system consstng of a spot market over a twonode network and a sngle energy forward contract. We formulate and analyze several models whch smulate ont dspatch of energy and transmsson resources coordnated by a system operator. The spot market s subect to network uncertanty, whch we model as a random capacty deratng of an mportant transmsson lne. Usng a duopoly model, we show that even for small probabltes of congeston (deratng), forward tradng may be substantally reduced, and the market power mtgatng effect of forward markets (as shown n Allaz and Vla, 1993) may be nullfed to a great extent. There s a spot transmsson charge reflectng transportaton costs from locaton of generaton to a desgnated hub whose prce s the underlyng for the forward contract. Ths allevates some of the ncentve problems assocated wth the forward market n whch spot-market tradng s resdual. We fnd that the reducton n forward tradng s due to the segregaton of the markets n the constraned state, and the absence of natural ncentves for generators to commt to more aggressve behavor n the spot market (the strategc substtutes effect). In our analyss, we fnd that the standard assumpton of no-arbtrage across forward and spot markets leads to very lttle contract coverage, even for the case wth no congeston. We present an alternatve vew of the market where lmted ntertemporal arbtrage enables temporal prce dscrmnaton by competng duopolsts. In ths framework we assume that all of the demand shows up n the forward market (or that the market s cleared aganst an accurate forecast of the demand), and the forward prce s determned usng a market clearng condton. 1. INTRODUCTION In the past few years, wholesale electrcty markets have gone through fundamental changes n the U.S. and around the world. 1 Electrcty ndustry restructurng began n Latn Amercan countres n the early 1980s, and more famously, n the Unted Kngdom n In the late 1990s, several U.S. states or control areas such as Calforna, Ths work was partally supported by the Consortum for Electrcty Relablty Technology Solutons on behalf of the Department of Energy, the Unversty of Calforna Energy Insttute, and NSF grant EPNES An earler verson of ths paper was presented at the Center for Research n Regulated Industres 22 nd Annual Eastern Conference, Skytop, Pennsylvana, May 21-23, See Enhorn (1994), Glbert and Kahn (1996), and Chao and Huntngton (1998) for surveys on the subect. 1

2 Pennsylvana-New Jersey-Maryland (PJM) Interchange, New York, and New England establshed markets for electrcty; and more recently, FERC Order 2000 has prompted several proposals for the establshment of Regonal Transmsson Organzatons (RTOs). Two key common aspects of the transton toward compettve electrcty markets n the U.S. and around the world, are a compettve generaton sector and open access to the transmsson system. However, there s consderable dversty among the mplementaton paths chosen by dfferent states and countres. The dfferences are reflected n varous aspects of market desgn and organzaton, such as groupngs of functons, ownershp structure, and the degree of decentralzaton n markets. The experence ganed from the frst wave of restructurng n places such as the Unted Kngdom, Scandnava, Calforna, and PJM, have led to several reassessment and revson proposals of varous market desgn aspects n these ursdctons. Two maor themes n market desgn have emerged n the restructurng process, and have been mplemented or currently proposed for the varous markets n the U.S (see Wlson, 1999 for an overvew of dfferent market archtectures). The frst one, reles on centralzed dspatch of all resources n the market, varatons of whch are mplemented n the PJM Interchange, New York, and New England (see Garber, Hogan and Ruff, 1994; Budhraa and Woolf, 1994). In ths desgn, an ndependent system operator runs a real-tme market wth centralzed dspatch. Blateral trades are allowed n ths system though they are purely fnancal n nature and do not get schedulng prorty. Blateral trades are charged locatonal prce dfferences n the real-tme market, and these can be hedged by some type of transmsson congeston contracts, whch are agan fnancal nstruments that guarantee the holder the prce dfferental between locatons specfed n the contract (see Hogan, 1992 and Harvey, Hogan and Pope, 1997). 2 The second desgn reles on a more decentralzed approach, at least n the day-ahead energy market. The verson that was orgnally mplemented n Calforna had two separate enttes, a Power Exchange (PX), whch was one of many short-term forward markets, and an ndependent system operator (ISO), whch managed real-tme operatons (see Blumsten and Bushnell, 1994; Wlson, 1997). 3 The verson mplemented n Texas reles on blateral tradng and prvate exchanges for day-ahead energy tradng, and some of the emergng RTOs also rely on varous forms of decentralzed day-ahead markets. The key feature of ths scheme s that day-ahead energy tradng and settlements are based on a smplfed commercal model of the transmsson network where nodes are grouped nto few zones, and only few nterzonal transmsson constrants (deemed commercally sgnfcant - CSC) are enforced (.e., prced) on day-ahead schedules submtted to the system operator. Congeston on CSCs can be hedged through fnancal or physcal rghts on these constraned nterfaces. Such zonal aggregaton facltates lqudty of the dayahead market but t allows schedulng of transactons that are physcally mpossble to mplement due to relablty constrants. A centrally coordnated real-tme physcal market n whch operatonal decsons are based on an accurate operatonal model of the transmsson grd corrects these nfeasbltes. The extent to whch fnancal settlements n the real-tme market reflect operatonal realtes s a hghly debated ssue that s not yet resolved n many of the emergng RTOs. The debate concerns the extent to whch the costs of correctng nfeasble schedules should be drectly assgned to those that cause such nfeasbltes, as opposed to socalzng these costs through unform or load-share based uplft charges. 2 Current mplementatons at PJM, New York and New England allow physcal blateral contracts, whch are nterpreted as zero offers on the necton sde and nfnte bds on the load sde. 3 The PX was dssolved n January,

3 Theoretcal analyss and emprcal evdence suggests that forward tradng reduces the ncentves of sellers to manpulate spot market prces by reducng the senstvty of sellers' profts to spot prce fluctuatons. Thus, forward tradng s vewed as an effectve way of mtgatng market power at real tme. It s also argued that settng prces at commtment tme provdes ncentves for accurate forecastng and provdes ex-ante prce dscovery that facltates tradng, helps operatons and mproves system relablty at reduced cost. There s, however, only lmted theoretcal analyss to support these assertons. Furthermore, t s not clear to what extent supplers wth market power have an ncentve to engage n forward transactons. The lmted amount of contractng n Calforna (even after the ban by the Calforna Publc Utlty Commsson was removed) and the collapse of the Calforna Power Exchange (PX) may suggest that some form of regulatory nterventon (short of drect government purchases) mght be requred to nsure that the publc s protected by an adequate amount of forward contracts. The man goal of ths paper s to examne the extent to whch a two-settlement system facltates forward tradng. In other words, we quantfy how sellers wll allocate ther producton between forward and spot sales when that decson s endogenous. We also examne the welfare and dstrbutonal mplcatons of such a system n the presence of network uncertanty and generator market power. We model the centralzed dspatch-type markets descrbed above (see Kamat and Oren, 2002 for models and analyss of systems wth separated electrcty and transmsson markets). As a benchmark for comparson we use a sngle-settlement nodal model. 4 The answers to these questons depends on the extent to whch speculatve trades can arbtrage the dfference between forward prces and the expected spot prces. In the absence of such arbtrage, generators may amplfy ther market power through strategc ntertemporal prce dscrmnaton. In order to examne the effects of such dscrmnaton we wll relax the prevalng no arbtrage assumpton n the analyss of multsettlement markets and ntroduce an alternatve sequental market clearng hypothess. We perform our analyss under the assumpton that generators use Cournot conectural varatons when makng decsons. Whle ths s a common assumpton n sngle perod models, there s an ongong debate on ts relevance n two-settlement systems. We recognze that our results may change based on the conectural varaton assumed. From a computatonal pont of vew, the Cournot assumpton makes the problem relatvely tractable whle retanng the most mportant features such as network representaton (see Wu et al., 2002; Wu and Klendorfer, undated; and Wu et al., undated for analyses buldng on dfferent assumptons). 5 The remander of the paper s as follows. The next secton provdes a revew of the relevant lterature on spot market modelng, modelng nteractons between spot and contract markets, and approaches to transmsson prcng. Secton 3 presents formulatons of the varous market desgns analyzed n ths study. In Secton 4, we analyze the mpact of network uncertanty n a smple two-node example. Secton 5 provdes some concludng remarks and addresses future work. 4 We gnore transmsson contracts n ths study, and focus on a market wth a sngle zone. 5 A recent study for the Calforna System Operator where modest network representaton and dfferent conectural varatons were assumed faced severe convergence problems. 3

4 2. LITERATURE REVIEW We revew lterature on electrcty market modelng, both wth and wthout transmsson constrants, and models wth contracts. Whle some electrcty market models have attempted to nclude transmsson constrants, models wth two-settlement systems (or forward energy contracts) usually treat the electrcty market as f t s delverable at a sngle locaton. We also revew the market desgns n greater detal specfcally wth respect to transmsson prcng Electrcty Market Models Schweppe et al. (1988) orgnated the theory of compettve electrcty locatonal spot prces. Gven costs of all generators on the network, demand, and network topology, locatonal prces can be calculated usng an optmal power flow model, whch seeks to mnmze the total cost of generaton. In a decentralzed envronment, fully compettve envronment, these prces can elct the optmal quanttes from compettve agents. Dfferences n locatonal prces reflect dfferences n equlbrum margnal costs at varous locatons, and can be used to set transmsson charges for blateral contracts (Schweppe et al., 1986; Hogan, 1992). Later studes, however, have consdered the effect of generator market power n electrcty markets. Equlbra wth two conectural varatons, supply functon equlbra (see Klemperer and Meyer, 1989), and Cournot-Nash equlbra have been examned Models wthout Transmsson Constrants Green and Newbery (1992), use supply functon equlbra to descrbe the electrcty spot market n England and Wales soon after deregulaton n In a supply functon equlbrum (SFE), each frm submts a non-decreasng supply functon specfyng the quantty t s wllng to provde at a gven prce. These functons can be derved as solutons to a set of coupled dfferental equatons. Green and Newbery fnd that n the short-term (untl new entry that was proposed was set up), the ncumbents had sgnfcant market power, and large deadweght losses could result f they compete n a SFE. They also argue that the amount of planned entry s more than s socally desrable, and could cause substantal deadweght losses n the future due to the unnecessary expense n nvestment. Bolle (1992) also consders several models of SFE n whch consumers react to a fxed prce, to average spot prces, and drectly to spot prces. He allows for backward bendng supply functons, and fnds a contnuum of equlbra n all cases. He recommends that consumers be drectly exposed to spot prces as ths s the only model n whch ncreasng the number of frms results n more compettve behavor. Bolle (2001) extends the earler analyss to nclude demand sde bddng. In a detaled analyss, he derves power seres solutons for supply functon 6 One of the arguments n favor of deregulaton of the generaton sector was that generators would compete as Bertrand olgopolsts and ths would result n compettve prces. Also, t was argued that the threat of entry by small and effcent combned cycle gas powered capacty would brng the necessary dscplne to the market. In the mmedate years after deregulaton, however, a duopoly exsted, wth two frms -- Natonal Power and Powergen -- controllng 80 percent of the generaton capacty and wth substantal prce settng power. In the daly market run by the grd operator, Natonal Grd Company, these frms submtted a supply schedule for each generator under ther control. The grd operator aggregated these schedules, and usng optmzaton software calculated a system margnal prce, whch was pad to all generators. Other payments for start-up costs and capacty avalablty were also made. 4

5 equlbra n supply and demand functons, and analyzes restrctons on free parameters of the soluton n order to get meanngful solutons wth postve prces and quanttes, upward slopng supply functons and downward slopng demand functons, and postve excess supply to meet autonomous demand. Bolle fnds that these restrctons may mply that prces may n general be bounded away from margnal cost and computes lower bounds for some cases. Andersson and Bergman (1995) calculate Bertrand and Cournot-Nash equlbra under varous assumptons n an ex-ante analyss of the Swedsh electrcty market. They fnd that deregulaton s not a suffcent condton for lower equlbrum prces gven the structure of the market at that tme (two frms controlled seventy-fve percent of the market). They fnd that ncreasng the number of frms n the market to about fve equal sze frms would brng dscplne to prces, as would hgher demand elastcty and monopsony power. Newbery (1995) examnes equlbra wth capacty constrants, and agan consders ssues of entry nto the England and Wales market, whle Green (1996) examnes how many frms would be requred for a more compettve market. Rudkevch, Duckworth and Rosen (1998) and Bohn, Klevorck and Stalon (1999) apply these technques to U.S. markets. Rudkevch et al. propose an teratve scheme for lnear margnal costs, whch converges to the unque lnear SFE for ths case. Baldck, Grant and Kahn (2000) generalze ths to the case of asymmetrc plants wth affne margnal costs, where supply functons can be lnear or pecewse lnear. They also propose an adhoc approach to deal wth capacty constrants n ths case. von der Fehr and Harbord (1993) consder the electrcty market n England and Wales as a multunt aucton and examne equlbra under capacty constrants. They fnd that when frms have to bd dscontnuous step functons nstead of contnuous supply functons there are no pure strategy equlbra comparable to SFE equlbra. They fnd mxed strategy equlbra nstead; though prcng above margnal costs s seen n many equlbra they derve. Marín Urbe and Garca-Daz (2000) extend von der Fehr and Harbord s model to allow for any technology mx and elastc demand n an applcaton to the Spansh market. In another applcaton to the Spansh electrcty market, Ramos, Ventosa and Rver (1998) combne a tradtonal producton cost model wth equlbrum constrants for modelng proft maxmzng by ndvdual frms, and approxmate a decentralzed equlbrum n an optmzaton wth equlbrum constrants framework. They mantan a detaled representaton of the electrc system operaton by consderng ramp-rates, mnmum up and down tmes, and operatonal features of hydro plants. However, they compute lnear prces,.e. there s a unform prce pad to all generaton n a perod, and so, total amount pad to generaton across perods s lnear n prce for any perod. It s not clear whether n a decentralzed stuaton such lnear equlbra exst due to the non-convextes n the cost-structure. 7 7 See Johnson, Oren and Svoboda (1997). 5

6 Models wth Transmsson Constrants Most of the models wth transmsson constrants assume the Cournot conectural varaton. 8 An mportant modelng choce n these models s the assumpton on whether agents wll game transmsson markets. Ths may have an mpact on the amount of congeston rent pad to transmsson rghts holders. Assumng that agents wll game the market, however, leads to non-convex problems wth possbly multple equlbra (see Oren, 1997a; Cardell, Htt and Hogan, 1997 among others). 9 On the other hand, f the man purpose of the model s to model generator behavor n the energy market, assumng that agents act as prce takers n the transmsson market allows the models to be solved as complementarty problems or varatonal nequaltes (see Hobbs, 2001; Smeers and We, 1997b). Cardell, Htt and Hogan (1997) consder a model wth Cournot generators who may own plants at multple locatons on a network, and a compettve frnge that takes the strategc generators quanttes as gven, and act as prce takers n the spot market. A complcatng feature of ths model s that wth the ntroducton of a compettve frnge, a gven strategy profle of the generators may not lead to a unque outcome n the spot market. Another feature s that the strategy sets, and not ust the obectve functon values, of the generators depend on the actons chosen by other generators. Ths type of game s called a generalzed Nash game (see Harker, 1991) and can have multple equlbra. Cardell et al. use an teratve procedure, solvng a relaxed form of each Cournot generator s nonconvex optmzaton problem n sequence, and report that a nonlnear solver always found solutons that satsfed a Cournot equlbrum test. A sgnfcant result comng out of ther work s that generators ownng multple unts on a network may not necessarly reduce output n all of them. In fact, ncreasng output on some generators may gve t a strategc advantage by forcng out some competton on another part of the network, and due to transmsson constrants, allow t to earn more profts on ts remanng capacty (also see Hogan, 1997). Hobbs, Metzler and Pang (2000) solve a smlar problem, where generators have a scalar ntercept mark-up strategy, usng an nteror pont algorthm. Ther model does not consder a compettve frnge. 10 Berry et al. (1999) consder the effect of network structure and capacty lmts on compettve behavor n lnear supply functons. They retan the assumpton that generators game the transmsson network. Usng two and four node network examples, they show that effectve transmsson congeston rent can be reduced through strategc bddng n supply functons. Other effects such as decreased effcency from decreasng concentraton are also observed n a four node network. Borensten, Bushnell and Stoft (1999) show that nteractons among Cournot generators n the presence of a transmsson constrant can be qute complex. They show that n a spatally separated market wth a symmetrc duopoly, and wth a small enough transmsson lne, no pure strategy Cournot equlbra exsts. Ths s due to the fact that there are dscontnutes n the response functons of the generators. Along the response functon, one generator produces a constant amount, congestng the transmsson lne n the drecton of the other market untl the 8 See Smeers (1997) for a dscusson on computable equlbrum models of restructured electrcty markets. A varaton on the Cournot assumptons s to model supply functon equlbra usng a scalar or two-parameter strategy vector (see Berry et al., 1999; Hobbs, Metzler and Pang, 2000; Day, Hobbs and Pang, 2001). 9 See Luo, Pang and Ralph (1996) for a comprehensve analyss of such problems. 10 Havng a compettve frnge would mply that transmsson prces reflect the opportunty cost of margnal energy trades. Cournot generators would therefore have less control over transmsson revenues that the system operator collects. Assumng an ntercept mark-up strategy gves the suppler n ths paper an addtonal degree of freedom to manpulate congeston revenues. 6

7 other generator s producton reaches a threshold level, at whch pont t ncreases ts output proportonally. At another threshold level, the frst generator abandons ths strategy and reverts to a defensve strategy wth smaller producton than n the frst case mentoned above. The authors also analyze cases where passve-aggressve or multple equlbra can exst. The above approach of solvng generators optmzaton problem sequentally mples that generators wll take nto account how ther actons affect transmsson prces. Some other models do away wth ths complcaton by assumng that generators do not game the transmsson system. Ths removes the non-convexty from each generator s optmzaton problem. Frst order condtons for all the generators can now be aggregated along wth those of transmsson owners, and the equlbrum can be solved as a complementarty problem. We and Smeers (1997) consder a Cournot model wth regulated transmsson prces (Smeers and We, 1997b consder a model wth a transmsson market). They solve varatonal nequaltes to determne unque long-run equlbra n ther models. Smeers and We (1997a) consder a separated energy and transmsson market, where the system operator conducts a transmsson capacty aucton, and power marketers purchase transmsson contracts to support blateral transactons. They fnd that such a market converges to the optmal dspatch for a large number of marketers. Borensten and Bushnell (1999) use a grd search algorthm to converge teratvely to a Cournot model wth data on the Calforna market. Hobbs (2001) uses lnearly decreasng demand and constant margnal cost functons, whch result n lnear mxed complementarty problems, to solve for such Cournot equlbra. In a blateral market, Hobbs analyzes two types of markets, wth and wthout arbtrageurs. In the market wthout arbtrageurs, non-cost based dfferences can arse because the blateral nature of the transactons gves generators more degrees of freedom to dscrmnate between electrcty demand at varous nodes. Ths s equvalent to a separated market as n Smeers and We (1997a). In the market wth arbtrageurs, any non-cost dfferences are subect to arbtrage by traders who buy and sell electrcty at nodal prces. Ths equlbrum s shown to be equvalent to a Cournot-Nash equlbrum n a POOLCOtype market Emprcal Work on Market Power Emprcal evdence to support the hypothess that electrcty markets are susceptble to market power can be found n Borensten, Bushnell and Wolak (1999), Wolfram (1998 and 1999), Mansur (2001), and Puller (2001). These studes focus on the U.K., Calforna and PJM markets. Borensten, Bushnell and Wolak (1999) calculate prce cost margns n Calforna by estmatng expected aggregate margnal cost curves for thermal generaton. They use system-wde demand as the market clearng quantty, and the unconstraned PX prce as the market-clearng prce. In calculatng the margnal cost curve, they account for must-take generaton, hydroelectrc load, mports etc., and for thermal capacty, they perform Monte Carlo smulaton to calculate expected margnal cost at the net market clearng quantty for thermal capacty. 11 They fnd that overall prces averaged about 15% above the compettve level for the summer of Wolfram (1999) and Mansur (2001) use smlar methodology for the U.K. and PJM markets, respectvely. Puller (2001) uses frm-level data to analyze prcng behavor n the frst two years of the 11 However, they do not nclude nter-temporal costs arsng from unt-commtment constrants. 7

8 Calforna market. Puller tests both statc and dynamcs models of olgopoly, and fnds evdence that generatng frms used statc market power n ths perod Electrcty Market Models wth Spot and Contract Markets Work n ths area has focused on the welfare enhancng propertes of forward markets and the commtment value of forward contracts. Theoretcal studes have shown that for certan conectural varatons, forward markets ncrease economc effcency through a prsoners dlemma type of effect (see Allaz, 1992, and Allaz and Vla, 1993). 12 Other theoretcal lterature has analyzed the commtment value of contracts as barrers to entry (see Aghon and Bolton, 1987). Applcatons to electrcty markets seem to focus manly on these two ssues Theory The basc model n Allaz (1992) s that producers meet n a two perod market where there s some uncertanty n demand n the second perod. In the frst perod, producers buy or sell contracts and a group of speculators take opposte postons. In the second perod, a non-compettve market wth Cournot conectures s modeled. A no-arbtrage relaton between forward and expected spot prces decdes the forward prce. If all speculators are rsk averse, the forward prce contans a rsk premum, otherwse f one or more rsk neutral speculators are present, the forward prce s an unbased estmator of the spot prce. Allaz shows that generators have a strategc ncentve to contract forward f other producers do not. Ths result can be understood usng the strategc substtutes and complements termnology of Bulow, Geneakoplos and Klemperer (1985). Essentally, the Cournot conectural varaton mples that producton quanttes are strategc substtutes. Ths s because an ncrease n one producer s quantty has a negatve effect on the other s margnal proftablty, and thus ts best response s lower than was prevously optmal. The avalablty of the forward market makes a partcular producer more aggressve n the spot market. Due to the strategc substtutes effect, ths produces a negatve effect on ts compettor s producton, and the resultng prce decrease s not as severe as t would have been f ts compettor had not reacted. The producer wth access to the forward market can therefore use ts forward commtment to mprove ts proftablty to the detrment of ts compettor. 13 Allaz shows, however, that f all producers have access to the forward market, t leads to a prsoners dlemma type of effect, reducng profts of all producers. Socal welfare measured as the sum of consumer and producer surpluses s hgher than n a sngle-settlement case wth producers behavng à la Cournot. Allaz ponts out that the results are very senstve to the knd of conectural varaton assumed, and shows that Cournot and market-sharng conectural varatons n the forward market lead to very dfferent results. Allaz and Vla (1993) extend ths result to the case where there s more than one tme perod where forward tradng takes place. For a case wth no uncertanty, they establsh that as the number of perods when forward tradng takes place tends to nfnty, producers lose ther ablty to rase market prces above margnal cost 12 Ths effect s not seen, for example, wth the Bertrand conectural varaton. 13 Bulow, Geneakoplos and Klemperer (1985) warn, however, that assumptons of lnearty on the demand often produces strategc substtutes, but that ths may no longer be true f demand s constant elastcty or nonlnear. 8

9 and the outcome tends to the compettve soluton. Haskel and Powell (1994) extend these results to general conectural varatons n the spot market. An mportant consderaton n electrcty markets s that generators meet n these markets almost on a daly bass. There s a rch lterature on repeated games, whch formalzes folk-theorem type results, n whch producers often can play collusve lookng outcomes n repeated settng whch secure them above-cournot profts. These results are senstve to assumptons such as observablty of past actons and the dscount factor. It would be of nterest to see what type of dscount factors are needed to reverse the forward markets are welfare enhancng results n ths lterature. Producers n the Allaz (1992) model do not have a commtment devce to stay out of the forward market, whch essentally reduces ther proftablty n the overall game. A repeated game settng may provde a way for producers to commt to keepng ther forward postons to a mnmum, thus reversng some of these results Applcatons von der Fehr and Harbord (1992) and Powell (1993) are early studes that nclude contracts, and examne ther mpact on an mperfectly compettve electrcty spot market, the U.K. pool. von der Fehr and Harbord (1992) focus on prce competton n the spot market wth capacty constrants and multple demand scenaros. They fnd that contracts tend to put downward pressure on spot prces. Although, ths provdes dsncentve to generators to offer such contracts, there s a countervalng force n that sellng a large number of contracts commts a frm to be more aggressve n the spot market, and ensures that t s dspatched n to ts full capacty n more demand scenaros. They fnd asymmetrc equlbra for varable demand scenaros where such commtment s useful. Powell (1993) explctly models recontractng by Regonal Electrcty Companes (Recs.) after the maturaton of the ntal portfolo of contracts set up after deregulaton. He adds rsk averson on the part of Recs. to the earler models. Generators act as prce setters n the contract market, but compete n a Cournot equlbrum n the spot market. The Recs. set quanttes n the contract market. He shows that the degree of coordnaton has an mpact on the hedge cover demanded by the Recs., and ponts to a free rder problem whch leads to a lower hedge cover chosen by the Recs. Batstone (undated) consders the mplcatons of strategc behavor on the part of rsk-neutral generators faced wth cost uncertanty who contract wth rsk-averse consumers maxmzng mean-varance utlty. He shows that n equlbrum generators have an ncentve to ncrease the varance n the spot market prce to extract a larger forward premum, and ncrease profts by sellng more contracts. Newbery (1998) analyzes the role of contracts as a barrer to entry n the England and Wales electrcty market. Newbery extends earler work by modelng equlbra n supply functons n the spot market. For tractablty he assumes constant margnal costs, whch allow hm to derve analytcal solutons to the spot supply functons. He models rsk-neutral consumers wth a smlar market structure as n Powell. Newbery shows that f entrants can sgn base load contracts and ncumbents have enough capacty, the ncumbents can sell enough contracts to drve down 14 There s a large lterature on the commtment value of contracts, see e.g. Aghon and Bolton (1987) and Dewatrpont (1988) for early contrbutons. Most of ths lterature crtczes the use of Pareto-domnated equlbra at later stages n a mult-stage game n order to select Pareto-superor equlbra n the overall game. If agents can renegotate from a Pareto-domnated equlbra to some other equlbrum then the selecton of the Pareto-superor equlbrum s n queston. It s suggested that selected equlbra be renegotaton-proof. 9

10 the spot prce below the entry deterrng level. Newbery shows that ths could result n more volatle spot prces f producers coordnate on the hghest proft SFE. Capacty lmts however may mply that ncumbents cannot play a low enough SFE n the spot market and hence cannot deter entry. Green (1999) extends Newbery s model ncludng lnear margnal costs. An nterestng result s that when generators compete n SFEs n the spot market, an assumpton of Cournot conectural varatons n the forward market mples that no contractng wll take place unless buyers are rsk averse and wllng to provde a hedge premum n the forward market. 15 The author ponts out the ths s a functon of lnear SFEs derved n ths study, and not a general result for SFEs. Len (2001) extends these results by explctly modelng entry nto these markets. He shows that forward sales can deter excess entry, and ncrease economc effcency and long-run profts of a large ncumbent frm faced wth potental entrants Transmsson Prcng and Desgn of Transmsson Capacty Rghts Though we do not consder transmsson contracts n ths paper, the nteracton between forward transmsson markets (manly n the form of transmsson capacty rghts) and the spot energy market, and n partcular, the nfluence of generator market power on the value of such rghts has been studed n the lterature. The role of the system operator n provdng open-access to the transmsson network and prcng scarce transmsson resources (as per FERC Order 888, and more recently FERC Order 2000), and to ts extent of nvolvement n energy and other unbundled energy product markets has also been a hotly debated ssue over the past decade (see references n Kamat and Oren, 2002). In a compettve market wth centralzed dspatch, locatonal prces are calculated at every node n the network (Schweppe et al., 1988). Congeston rent s then ust the dfference n locatonal prces between any two locatons. Hogan (1992) shows that f transmsson rghts are fnancal rghts to these locatonal prce dfferences then ths maxmzes the value of the network. Under ths paradgm, he proves revenue suffcency of the system operator who provdes access,.e. the merchandzng surplus resultng from sellng and buyng power at nodal prces wll cover the payments to transmsson rghts holders. The natural type of transmsson rghts that go wth ths scheme are pont-to- pont rghts (see Harvey, Hogan and Pope, 1997). These rghts enttle the holder to the dfference n locatonal prces between two ponts specfed n the rght. For some of the proposed markets n the U.S. there are proposals that call for flow-based transmsson rghts (also called flowgate rghts or FGRs; see Chao and Peck, 1996 and 1997; Chao et al., 2000a). The dea s that n any electrcty network only a small number of transmsson lnes are expected to be congested, and f forward markets are establshed only for these commercally sgnfcant flowgates they wll be hghly lqud and provde adequate prce sgnals to nternalze network externaltes. Ths type of scheme also facltates blateral forward contractng. The nfluence of generator behavor on the market value of fnancal transmsson rghts has also receved attenton. Usng Cournot assumptons, Oren (1997) argues that generators at supply nodes wll have enough market power to capture the entre market value of passve or fnancal transmsson congeston contracts usng two and three node examples. He argues that wth actve or physcal rghts, and parallel tradng n energy and transmsson markets, such abuse of market power wll be lmted; Stoft (1999) argues to the contrary, and suggests that fnancal 15 Ths result can also be understood n terms of Bulow et al. s results. In Green s model, a partcular frm s contract poston has no effect on ts compettor s spot market strategy, whch means that there s no strategc substtutes effect. 10

11 rghts do mtgate market power under slghtly dfferent assumptons. Joskow and Trole (2000) provde a comprehensve analyss of how the allocaton of transmsson rghts affects markets wth generator and consumer market power. They fnd that the extent of the effects depends on the mcrostructure of the transmsson rghts markets and the dstrbuton of market power. They fnd that purely physcal rghts have worse welfare propertes than fnancal rghts, but ntroducng a use-or-lose feature (whch prevents wthholdng of physcal capacty, but stll honors the fnancal enttlement of the rght) may help allevate some of these adverse propertes. Daxhelet and Smeers (2002) consder transmsson prcng ssues n the context of cross-border electrcty trade. 3. FORMULATION Our formulatons try and capture several aspects of current electrcty market desgns that have been prevously modeled n solaton. We focus on two-settlement systems n the presence of network uncertanty and market power. We model network uncertanty n the form of a random capacty deratng of an mportant lne n the transmsson network. Studes wth market power usually consder sngle-settlement systems, whle the lterature modelng nteractons between spot and forward markets does not consder transmsson constrants. As our focus s on understandng the mechansms that drve our results, we analyze the problem wth the help of several llustratve examples on smple two- and three-node networks. We formulate the problem as a two perod game where generators use a Cournot conectural varaton n the spot market (perod 2). 16 We assume that generators take transmsson prces as gven and do not try to game the transmsson system (Hobbs, 2001, and Smeers and We, 1997a make such an assumpton). There s a probablty r that one of the transmsson lnes s derated to a level that t wll be bndng n the spot market. In perod 1, we model a forward market wth a sngle contract for energy delvered n perod 2. In a two-settlement system t becomes necessary to descrbe accurately the commodty, or the commodty prce n case of fnancal contracts, underlyng the forward contract. Rather than choosng an arbtrary spatal locaton, we choose the underlyng prce as a vrtual hub-prce equal to the demand-weghted average spot prce. As ths s an energy contract, generators are charged a spot transmsson charge for energy delvered at ther locaton, whch s equal to the dfference between the hub-prce and the nodal prce at the generator s locaton. No transmsson contracts are avalable to hedge ths uncertan cash flow. In the presence of speculators who trade between the markets, the forward prce wll converge to the demand-weghted expected spot prce (assumng rskneutralty and zero nterest rates), and ths fact s used to determne forward prces n ths case. In our example, we fnd that ths model predcts relatvely small aggregate postons n the forward market. 17 There seems to be ample emprcal evdence that generators cover a large porton of ther spot sales under forward contracts. There s also evdence that fnancal dervatves markets n electrcty are generally llqud, and tradng n these markets, to the extent t exsts, has been much less than n comparatve markets for other commodtes. In the absence of speculators that can explot arbtrage opportuntes between the forward and spot market prces, generators can exercse ther market power for ntertemporal prce dscrmnaton and ncrease ther profts 16 We are not aware of any study that derves a general supply functon equlbrum n presence of a transmsson constrants. 17 Ths may change, although to a small extent, wth the ntroducton of rsk-averson n the model. 11

12 by prcng forward contracts above the expected spot prce. Arbtragng such prce dfferences would requre speculators to take short postons n the forward market and cover ther postons n the spot market. Such arbtrage s consdered as very rsky gven the hgh volatlty of spot electrcty markets whch may explan the fact that we do not see much speculatve tradng of that sort. On the contrary, most speculatve tradng to the extent that t exst tends to nvolve long postons n the forward market whch wll further ncrease forward prces. Consequently, ntertemporal prce dscrmnaton wth hgher forward prces can be sustaned whch rases questons regardng the valdty of the Allaz-Vla, (1993) model whch rests on a no arbtrage assumpton between forward and spot prces. The lack of uncovered short postons for short-term forwards has been recently brought up n ltgaton at the FERC n support of the argument that market power n generaton extends to short-term forwards. There have been short forward postons that have been covered by nvestment n new generaton, however, ths only apples to delveres beyond 18 months or so (FERC, 2002). As an alternatve model, we explore a physcal market n whch all demand shows up n the forward market (or that the market s cleared aganst an accurate forecast of the expected demand), and the forward prce s determned usng a market clearng condton. Ths case can be seen as a purely physcal market, because n the presence of speculators who could arbtrage between forward and spot markets, such a system would not work. 18 Ths essentally relaxes the no-arbtrage condton, and provdes generators possessng market power wth the opportunty to ndulge n ntertemporal prce dscrmnaton, and extract a strategc premum n the forward market. We analyze the followng cases (a detaled descrpton of each case follows): Case A. Cost Based Economc Dspatch. Case B. Sngle-settlement Centralzed Market. Case C. Two-settlement System for Electrcty - No Arbtrage. Case D. Two-settlement System for Electrcty - Market Clearng. Case A. Ths s the welfare maxmzng 19 outcome and wll be the soluton to: (A) p p p = MC( q ) = p ( D ) q β = c a, q = p + D a for all. β for all β a, c a, λ c a D nodes wth generaton,. demand nodes,. = f c a for constraned lne a. for all nodes and hub ( ). (1) where, p, s the prce at node (we suppress the superscrpt for the state on energy prces and quanttes), q s the producton at node (t s assumed that each frm has a sngle plant), D s demand at node, λ ac s the multpler assocated wth lnk a 20 n state c, c {1, 2} an ndex set of states, β a, s the power transfer dstrbuton factor or the amount of power that wll flow over ths lne when 1 unt of power s transferred from node to a 18 Ths also assumes that demand behaves non-strategcally. 19 As stated above, we use the sum of consumer and producer surpluses as a welfare measure. 20 In our examples we assume that only the lne between nodes 1 and 2 s congested. 12

13 c reference node, and f a s the capacty of ths lnk n state c. Convexty restrctons on the demand and cost functons yeld unque outcomes. Case B. In ths case, we smulate a centralzed market outcome n a sngle-settlement system wth generators behavng à la Cournot (see Hobbs, 2001). In a centralzed market model, the system operator sets generaton and demand so as to maxmze gans from trade, and transmsson prces are set equal to the dfference n nodal prces. We assume that generators take transmsson prces as gven or that generators do not consder the nfluence of ther decsons on transmsson prces. An equlbrum of ths sngle-settlement system can be paralleled to an equlbrum of the followng two stage game. In the second stage of ths game, the system operator arbtrages any dfferences n energy prces that are not based on cost, such that n the resultng equlbrum, there s no spatal dscrmnaton n energy prces,.e. the prce dfference between two nodes s exactly equal to the transmsson charge for transferrng energy between the two nodes. In the frst stage, generators antcpate ths arbtrage and compete n a Cournot-Nash manner. Each generator wll solve the followng constraned optmzaton problem n a centralzed market: (B), 1 n 1 p q p Max q D, K, D, p, K, p = p ( D ) + k q k = p + = a n Π for D c c β a, λa = p q all nodes C ( q ) for all nodes and hub ( c Here λ a s to be nterpreted as the multpler assocated wth the system operator s problem whch the generators take as gven,.e. t s a parameter of the above optmzaton problem. The equlbrum for the game can be solved by collectng the two frst order necessary condtons (FONCs) along wth the constrants of the problem, and the followng set of nequaltes and complementary slackness condtons from the system operator s problem: (Ba) c c β a, q β a, c c ( β a, q β a, D D f c a f c a for all a c a ) λ = 0 for all a. In the case wth quadratc demand and cost functons, the equlbrum problem s a lnear (mxed) complmentarty problem (LCP) (mxed due to the equalty constrants). Convexty restrctons on the demand and cost functons yeld unque equlbrum ponts. ). (2) (3) Case C. In ths case, we assume that the system operator operates a sngle forward market for all demand wthn the zone wth a delvery requrement on forward transactons. Ths mples that all transactons that are dspatched n the spot market are charged the spot transmsson charge (see Chao et al., 2000b). Ths provdes ncentves for generators to avod what s called a DEC game n markets where such aggregaton s done n the forward market, e.g. the now defunct Calforna PX market (see Kamat and Oren, 2002 for an analyss of cases wth resdual spot markets,.e. markets where the spot transmsson charge only apples to the part of the forward transacton cleared n 13

14 the spot market). In a centralzed market, t becomes necessary to decde on a hub whch establshes the spot transmsson charge. Keepng n lne wth our earler assumpton for the settlement prce for a forward contract, we use the demand-weghted average prce as the hub prce. 21 Generators solve the followng optmzaton problem n the spot market: (C) D, K, D, p, K, p q, 1 n 1 p q p p = p + k = p hub Max = ( D q = ) + a p k k n Π k. = p c c β a, λa D D for D f all nodes f + p ( q for all nodes and hub f ) C ( q ) f ( ) ( p hub p ) Where p f c s the forward prce and f the forward poston of generator. Agan, λ a s a parameter n the above problem. As the hub prce ntroduces nonlnearty n the equlbrum condtons, the resultng spot market equlbrum problem s a non-lnear LCP. In order to calculate an equlbrum of the two-settlement system, we employ the noton of a subgame perfect Nash equlbrum (SPNE) (see Fudenberg and Trole, 1991). Ths says that n perod 1, generators wll correctly antcpate the reactons of all the agents movng n perod two. The generators wll therefore solve an expected proft maxmzaton problem n perod 1 (we assume that generators are rskneutral), subect to equlbrum constrants n the forward market, f any, and correctly antcpatng the optmal values from the spot optmzaton problem,.e. the non-lnear LCP wll appear as a constrant n the optmzaton problem solved by generators n perod We conduct a grd search to determne the optmal forward postons by numercally tracng reacton functons n the forward market. (4) Case D. Ths case s the formulated as Case C above except that the forward prce s determned by a market clearng condton,.e. p f = p(f 1 + f 2 ), where p(.) s the aggregate demand functon, and f 1 and f 2 are forward postons of respectve generators. 4. TWO-NODE EXAMPLE Consder the example n Fgure 1 wth a sngle generator at each node of a smple two-node network. Cost and demand functons are lnear as ndcated at each node. We assume there are two states of the world, one n whch the network does not have any transmsson constrants, and the other where the capacty of the lne onng node 1 and 2 s K MW. We model the two states usng a random varable whch takes two values θ (a large postve number) and 0 wth probablty r and 1-r, respectvely (θ s assumed to be large enough so that the transmsson lne between 21 Whle t s not common that forward commodty contracts are settled at a floatng prce (as opposed to the prce at a fxed delvery pont), ths s common practce n electrcty markets, e.g. the forward contract at the PJM Western hub s settled at a weghted prce based on 100 nodal prces. 22 In the general case, the generator s problem wll be non-convex due to the complementary slackness condtons mposed n the spot market equlbrum. As mentoned earler, f congeston patterns are easly predcted these can be dropped. 14

15 the two nodes s not congested n the cases we consder). The generator at node 1 s assumed to be low cost, and could run at output levels that the transmsson lne would not be able to sustan n the state of the world where ths capacty lmt s bndng (see Table 1 for data). c 1 + d 1 q 1 1 K + θ p 1 = a 1 - b 1 q 1 c 2 + d 2 q 2 2 p 2 = a 2 - b 2 q 2 Fgure 1: A Smple two-node network Table 1: Parameter Values for two-node example Parameter Value a1, a2 100 b1, b2 2 c1, c2 10 d1 1 d2 4 K 3 θ Large r Varable 4.1. No Congeston (Allaz and Vla, 1993) We frst analyze an example wth no congeston n the spot market (see Allaz and Vla, 1993). 23 Ths wll gve us a pont of departure from the lterature, and a bass for comparng how the presence of transmsson constrants affects behavor n two-settlement systems wth mperfect competton. We assume symmetrc demands for the two nodes n the system. Case A. In the optmum dspatch, margnal costs for both generators are equal to prce whch s determned by clearng the aggregate market for the two nodes (see equaton set (1)). Ths gves the maxmum surplus that can be generated n ths market. 23 Ths s the case when r = Pr{θ = 0} = 0 15

16 Case B. In the sngle-settlement case, generators compete n a Cournot-Nash game. As there are no transmsson constrants, each generator solves an smple unconstraned optmzaton problem (see problem (2) after substtutng the market clearng constrant nto the obectve). The standard frst order condton of equatng margnal revenues, wth respect to the resdual demand curve seen by a generator, to margnal costs apples drectly. These can be expressed as: p( q + q ) + q p () = C ( q ), = 1,2 ( ) where pq ( ) s the aggregate nverse demand functon. These equatons can be used to derve the reacton functons of the two generators n ths market,.e. the optmal producton quantty of a generator as a functon of the other generator s producton quantty. The equlbrum quanttes can be calculated as the pont of ntersecton of the two reacton functons. For our case of demands and margnal costs whch are lnear n quantty, the reacton functons are also lnear, and wll therefore result n a unque equlbrum (see Fgure 2). 24 The frst order condtons (5) can be rewrtten as: (5) p( ) C ( q ) p( ) = s ε for = 1,2 (6) where s q =, s frm s share of total producton, and q + q 1 p( ) ε = s the elastcty of aggregate demand p ( ) q at the aggregate producton quantty, q. The left hand sde s called the Lerner ndex for frm. 24 For nonlnear demand functons, there may be cases (such as wth convex demand functons) that one may have multple equlbra n the spot market. 16

17 80 Frm 2's Reacton Functon Frm 1's Quantt y Frm 1's Reacton Functon Frm 2's Quantty Fgure 2: Reacton Functons for Case B (no transmsson constrants). Case C. The two-settlement system case s solved as a two perod game. In the second perod, generators wll maxmze profts gven ther forward commtments. The frst order condtons n ths case wll be a modfed verson for those of the Cournot case (see problem (2)): p( q + q ) + ( q f ) p' ( ) = C ( q ) for, = 1,2( ) (7) where f s the frm s forward poston. Another way of dervng frst order condtons s by margnal analyss, whch looks at the beneft and cost of producng an addtonal unt settng the base level to the optmal producton quantty: p( q + q ) C ( q ) + ( q f ) p'( ) = 0 for, = 1,2( ) M arg nal Beneft M arg nal Cost Ths says that at the margn, the beneft of producng an extra unt, the prce-cost margn p( )-C ( ), should be equated to the externalty cost of producng that unt whch s the decrease n revenues from all nfra-margnal unts affected, (q -f ) p ( ). As generators are expected to take short postons n the forward market, prce cost margns n a two-settlement system wll be smaller than n the Cournot case. Thus, forward commtments result n greater producton n the spot market, and have the potental to ncrease the realzed surplus as compared to the snglesettlement case. Ths can be seen n the plot of the reacton functons whch go outward for larger forward commtments (see Fgure 3). (8) 17